Efficiency or yield is the relationship between the output power and the input power of a physical system. We can calculate efficiencies of machines, engines and equipment that process or convert one or more forms of energy.
For example, the efficiency of an electric motor, the efficiency of a combustion engine or the efficiency of an air conditioning unit.
When we talk about inverters for photovoltaic systems, efficiency refers to the ratio between the electrical output power and the electrical input power.
Ideally, we would like to have inverters with 100% efficiency, that is, no energy would be lost within the equipment – all energy supplied to the equipment input could be recovered at its output.
Optimal efficiency is not possible, but commercially available inverters already achieve efficiencies close to 99%, which is no small feat.
The concept of efficiency, illustrated in Figure 1, is relatively easy to understand. Things get complicated when different definitions arise around the same concept, as is often seen in photovoltaic inverter catalogs. And it becomes even more complicated when we discover that the efficiency of the equipment is not constant, but can vary according to its operating conditions.
Photovoltaic inverter efficiency curve
The efficiency curve or profile of a photovoltaic inverter is shown in Figure 2. We can immediately observe two things:
- The efficiency curve changes according to the inverter input voltage. In Figure 2 we observe curves for three different voltage values. The higher the input voltage, the lower the intensity of the electrical current that circulates through the inverter, which reduces its losses and increases its efficiency. When sizing a photovoltaic system, it is important to correctly size the photovoltaic strings to prevent the inverter from working with reduced voltage. Although the equipment can operate normally with any voltage value within the operating range specified in its data sheet, the efficiency curves show that the choice of working voltage has an impact on the equipment's performance – and consequently on the overall performance of the device. photovoltaic system.
- The efficiency curve is not a straight line. This means that the inverter's efficiency is not constant and depends on its operating point. In the graph in Figure 2 we observe the efficiency (%) on the vertical axis and the operating power on the horizontal axis. Operating power is expressed as the ratio of output power to rated power. In other words, the number 1 on the horizontal axis represents the operating point at the maximum (nominal) power of the equipment.
We can still make the following observations regarding the efficiency curves shown in the figure above: in each curve there is a portion that is approximately straight. In the examples above, this straight or flat portion of the curve is between 0,6 and 1,0. The best situation would be a flat (straight) curve in the range of 0 to 100%, which is impossible.
The further away from (or below) the rated power the operating point is, the lower the efficiency tends to be. The behavior described in the previous paragraph may vary from one piece of equipment to another, as illustrated in Figures 3 and 4.
In Figure 3, we observe the case of an inverter that presents very flat efficiency curves, with approximately constant values (and close to 97%) in the range of 40% to 100% of the nominal power – as long as it operates with an input voltage above 350V.
On the other hand, Figure 4 shows the case of an inverter that has maximum efficiency close to 40% of nominal power and reduced efficiency when the operating point approaches 100% of power.
Inverters with the behavior illustrated in Figure 3 are more desirable, as they can work with high efficiency (that is, they have less energy losses) over a wide operating range.
Throughout the day, months or any time interval that may be considered, the power of photovoltaic s changes depending on solar irradiance and temperature. Therefore, solar inverters rarely operate at a fixed power.
The behavior illustrated in Figure 4 is more observed in old equipment, the type that uses an internal transformer, practically extinct on the market. However, it is important to know the different efficiency profiles that can be found.
Photovoltaic inverters are not all the same and if operating efficiency is a choice criterion, the designer cannot fail to analyze the efficiency curves reported in the manufacturers' catalogues.
If we can establish a rule for choosing the ideal inverter for a project, leaving aside other aspects such as cost, number of inputs and other advanced features that can influence the choice, certainly a flat efficiency curve like the one in Figure 3 is a good request.
Maximum efficiency and weighted efficiency
Knowing how to interpret and analyze efficiency curves is not everything. You may have noticed that below each of the graphs in Figures 2 to 4 two values are shown: maximum efficiency and European efficiency.
The inverter's maximum efficiency is an important number, but it is not enough to qualify equipment or make comparisons between them. A piece of equipment may, for example, have maximum efficiency at a single operating point, but may have low efficiency at all other points. This is the case for inverters with efficiency profiles like the one in Figure 4.
To facilitate the qualification and comparison of inverters, the figure of average efficiency or weighted efficiency was created. As inverters do not always operate at their maximum efficiency point, the weighted efficiency value considers several operating points in the calculation.
This idea emerged in the European market, which is why we know it as “European efficiency”. European solar inverter efficiency is a weighted average of efficiencies calculated from an annual power distribution found in the European climate.
Considering that irradiance and temperature vary over the hours, days and months of the year, inverters operate part of the time at different power values, theoretically in a range that goes from 0 to 100% of their maximum power. .
European efficiency was created by the t Research Center (JRC), a European body that carries out research in the area of renewable resources, based on Italy's climate. European efficiency, calculated according to the equation below, is presented in virtually all photovoltaic inverter catalogs, as shown in Figure 5.
The equation performs the weighted average of several efficiency values (5% to 100%) considering the fraction of time that the inverter operates at each of these values.
European efficiency = 0,03 x Ef5% + 0,06 x Ef10% + 0,13 x Ef20% + 0,1 x Ef30% + 0,48 x Ef50% + 0,2 x Ef100%
It is to be expected that the efficiency calculation, as performed in the previous equation, may not reflect operating conditions outside of Europe. For warmer climates, with higher levels of insolation, the California Energy Commission (CEC) proposed a weighted average with different weights, as seen below.
CEC Efficiency = 0,04 x Ef10% + 0,05 x Ef20% + 0,12 x Ef30% + 0,21 x Ef50% + 0,53 x Ef75% + 0,05 x Ef100%
Research groups in other countries are proposing different weighted averages, adapted to their local climates. In India and Brazil, for example, weighted averages were proposed according to the equations shown below.
Indian efficiency = 0,248 × Ef10% + 0,121 × Ef20% + 0,092 × Ef30% + 0,159 × Ef50% + 0,215 × Ef75% + 0,162 × Ef100% + 0,003 × Ef120%
Brazilian efficiency = 0,02 x Ef10% + 0,02 x Ef%20 + 0,04 x Ef%30 + 0,12 x Ef%50 + 0,32 x Ef75% + 0,48 x Ef100%
Given the different climatic conditions found in each part of the world, it would be great if inverter catalogs presented efficiency values calculated according to the market in which they are sold. This, however, is not a reality and European efficiency is adopted worldwide as a reference by manufacturers.
Finally, we can observe in Figure 6 the behavior of the European weighted efficiency as a function of the inverter operating voltage. Just as the maximum efficiency of the equipment depends on the input voltage, we observe similar behavior for the weighted efficiency.
The graph in Figure 6 can offer good guidance for the design of photovoltaic strings (whose maximum power voltage – VMPP) depends on the number of modules connected in series. A bad choice can result in a loss of efficiency of up to 2% in the inverter, as shown in the example above.
References
- Brazilian efficiency of inverters for grid-connected photovoltaic systems. A. Pinto, R. Zilles, M. Almeida, Advances in Renewable Energy and the Environment, Vol. 15, 2011
- Weighted efficiency of SPV power converters/inverters in Indian composite climate. 32nd European Photovoltaic Solar Energy Conference and Exhibition, Vol. 32, 2016
- Efficiency and derating, Technical information (white paper), SMA, https://files.sma.de/s/WirkungDerat-TI-en-48.pdf
An answer
Marcelo, good night! I need some guidance, I bought a photovoltaic plant from a solar energy company and the contract we made was to deliver 3 inverters of 10 KW and 1 inverter of 6 KW and a total of 90 s of 525 W, but the company delivered 3 9 KW inverters and 1 7 KW inverter and they are saying that it will have the same energy generation, is that right? what do I do? If you could guide me I would appreciate it.